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Название: Mathematics made difficult
Автор: Linderholm С.
I found this book while browsing my university library 25 years ago. In a sea of titles like "Mathematics Made Easy/Simple/etc." this book stood out from the crowd. Now, my mathematical background would probably be categorized as "moderate" - the ordinary math taken by an engineering student, 3 years of calculus and differential equations. Advanced algebra, group and set theory, and topology are all beyond my understanding.
Since really understanding this book more or less depends on a knowledge of all of these, one might expect it to go above me. What I found instead was, in addition to enjoying the delightfully witty writing, I actually learned something about all these topics. Not that I remember much now, of course - but probably no less than I remember from most subjects I was actually enrolled in.
Example: Early in the book, he reproduces an imaginary Q&A in which the questioner relates that when he meets a mathematician at a party and he says "Well, I guess we've come a long way since 1+1=2", the mathematician makes a wry face. The author then, in answering the imaginary questioner, takes an entire chapter explaining exactly how complicated 1+1=2 really is. You have to start with what does "1" mean, for example. This leads to mathematical constructs I had never dreamed of simply to understand what numbers and counting are.
In summary, this is a wonderful book for anybody with at least an ordinary college-level understanding of math, and I hope somebody reprints it.